The memristor was originally proposed as a passive circuit element that provides a relationship between charge, current, voltage, and/or magnetic flux that complements the relationships provided by the resistor, the capacitor, and the inductor. In particular, a memristor is a two-terminal circuit element that has a memristance M(q) that depends on the net charge q that has passed through the memristor, and the voltage V across a memristor is equal to the product of the memristance M(q) and the current I through the memristor, i.e., V=M(q)I. Fabrication of memristors and other memristive devices has been impractical until recently. Some of the first practical memristive devices are described in U.S. Pat. App. Pub. No. 2008/0090337, entitled “Electrically Actuated Switch,” to R. Stanley Williams. These memristive devices utilize the behavior of nanoscale materials, particularly, a thin film of a material such as titanium dioxide between two electrodes. The memristive elements can currently be fabricated with feature sizes on the order of about 10 nm.
In another technology, a spatial electro-optical amplitude modulator can control the spatial distribution of the intensity and/or the phase of light over an area and thereby form an image or a pattern of illumination represented by electronic control signals. A backlit liquid crystal display (LCD), for example, contain pixels that are arranged in an array, and an image can be formed across the area of the array by applying electrical signals respectively to the pixels to control the light intensities transmitted through the pixels in the LCD. LCDs are well suited for displays viewed by the human eye. However, other uses of images or illumination patterns such as in photolithographic processes often require pixels sizes that are too small to be directly created using current LCD technology. Further, LCD devices are currently unable to modulate light with short wavelengths, such as ultraviolet (UV) light, and short wavelength light is needed or desirable for illumination involving feature sizes smaller than about 1 μm. LCD pixels also have response times on the order of a millisecond, which may be too slow for many uses.
Use of the same reference symbols in different figures indicates similar or identical items.